Course Descriptions

MAGY.6223I Elements Of Real Analysis II
3 Points, Tuesdays, 5:007:30PM, Yisong Yang
Description TBA 
MAGY.7043I Linear Algebra II
3 Points, Thursdays, 5:007:30PM, Gaoyong Zhang
Description TBA 
MATHGA.1002001 Multivariable Analysis
3 Points, Mondays, 5:107:00PM, Deane Yang
Description:
Linear and multilinear algebra. Differentiation and integration in several variables. Introduction to manifolds, tangent and cotangent bundle. Vector fields, differential forms, exterior derivative. curves, Integration of differential forms on a manifold, Stokes' Theorem.
Textbook:
Spivak, Calculus on Manifolds 
MATHGA.1420001 Introduction To Math Analysis II
3 Points, Thursdays, 5:107:00PM, Aaditya Rangan
Description:
This course studies measure theory and integration in Euclidean and abstract spaces. The topics of the course include Lebesgue measure, Lebesgue measurable functions, Lebesgue integration, LebesgueStieltjes measure and integral, general measure theory, Caratheodory's theorem, measurable functions, convergence in measure, Egoroff's and Lusin's theorems, integration in general measure spaces, monotone and dominated convergence theorems, FubiniTonelli theorem, LebesgueRadon
Nikodym theorem, and L^p spaces. Textbooks:
1. Real Analysis, by H.L. Royden and P.M. Fitzpatrick.
2. Real Analysis, by G.B. Folland.

MATHGA.1420002 Introduction To Math Analysis II
3 Points, Thursdays, 7:108:25PM, TBA
Description TBA 
MATHGA.2012002 Advanced Topics In Numerical Analysis: Convex And Nonsmooth Optimization
3 Points, Wednesdays, 5:107:00PM, Michael Overton
Description:
This class will be an introduction to the fundamentals of parallel scientific computing. We will establish a basic understanding of modern computer architectures (CPUs and accelerators, memory hierarchies, interconnects) and of parallel approaches to programming these machines (distributed vs. shared memory parallelism: MPI, OpenMP, OpenCL/CUDA). Issues such as load balancing, communication, and synchronization will be covered and illustrated in the context of parallel numerical algorithms. Since a prerequisite for good parallel performance is good serial performance, this aspect will also be addressed. Along the way you will be exposed to important tools for high performance computing such as debuggers, schedulers, visualization, and version control systems. This will be a handson class, with several parallel (and serial) computing assignments, in which you will explore material by yourself and try things out. There will be a larger final project at the end. You will learn some Unix in this course, if you don't know it already. Prerequisites for the course are (serial) programming experience with C/C++ (I will use C in class) or FORTRAN, and some familiarity with numerical methods.

MATHGA.2020001 Numerical Methods II
3 Points, Tuesdays, 5:107:00PM, Jonathan Goodman
Description:
This course will cover fundamental methods that are essential for the numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in numerical computing; computer programming assignments in MATLAB will form an essential part of the course. The course will introduce students to numerical methods for (1) ordinary differential equations (explicit and implicit RungeKutta and multistep methods, convergence and stability); (2) elliptic partial differential equations such as the Poisson eq. (finite difference, finite element and integral equation methods); (3) parabolic and hyperbolic equations such as the heat or wave equation (finite difference and finite volume methods). We will also discuss spectral methods and the FFT, exponential temporal integrators, and multigrid iterative solvers.

MATHGA.2048001 Scientific Computing In Finance
3 Points, Mondays, 7:109:00PM, Richard Lindsey and Mehdi Sonthonnax
Prerequisites:
Risk and Portfolio Management, Financial Securities and Markets, and Computing in Finance.Description:
This is a version of the course Scientific Computing (MATHGA 2043.001) designed for applications in quantitative finance. It covers software and algorithmic tools necessary to practical numerical calculation for modern quantitative finance. Specific material includes IEEE arithmetic, sources of error in scientific computing, numerical linear algebra (emphasizing PCA/SVD and conditioning), interpolation and curve building with application to bootstrapping, optimization methods, Monte Carlo methods, and the solution of differential equations.Please Note: Students may not receive credit for both MATHGA 2043.001 and MATHGA 2048.001

MATHGA.2071001 Machine Learning & Computational Statistics (1st Half Of Semester)
1.5 Points, Thursdays, 7:109:00PM, Ivailo Dimov
Prerequisites:
Multivariate calculus, linear algebra, and calculusbased probability. Students should also have working knowledge of basic statistics and machine learning (such as what is covered in Data Science & DataDriven Modeling). 
MATHGA.2110001 Linear Algebra I
3 Points, Tuesdays, 5:107:00PM, Tyler Chen
Prerequisites:
Undergraduate linear algebra or permission of the instructor.
Description:
Linear spaces, subspaces. Linear dependence, linear independence; span, basis, dimension, isomorphism. Quotient spaces. Linear functionals, dual spaces. Linear mappings, null space, range, fundamental theorem of linear algebra. Underdetermined systems of linear equations. Composition, inverse, transpose of linear maps, algebra of linear maps. Similarity transformations. Matrices, matrix Multiplication, Matrix Inverse, Matrix Representation of Linear Maps determinant, Laplace expansion, Cramer's rule. Eigenvalue problem, eigenvalues and eigenvectors, characteristic polynomial, CayleyHamilton theorem. Diagonalization.
Text:
Lax, P.D. (2007). Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts [Series, Bk. 78]. Linear Algebra and Its Applications (2nd ed.). Hoboken, NJ: John Wiley & Sons/ WileyInterscience. 
MATHGA.2120001 Linear Algebra II
3 Points, Wednesdays, 5:107:00PM, Deane Yang
Prerequisites:
Linear Algebra I or permission of the instructor.
Description:
Review of vector spaces, linear maps, determinant, spectral theory. Inner product spaces, Schur representation, polar and singular value decomositions, MoorePenrose pseudoinverse. Dual vector spaces and tensors.
Text:
Treil, Linear Algebra Done Wrong 
MATHGA.2140001 Algebra II
3 Points, Tuesdays, 11:0012:50PM, Alena Pirutka

Description:
Representations of finite groups. Characters, orthogonality of characters of irreducible representations, a ring of representations. Induced representations, Artin’s theorem, Brauer’s theorem. Representations of compact groups and the PeterWeyl theorem. Lie groups, examples of Lie groups, representations and characters of Lie group. Lie algebras associated with Lie groups. Applications of the group representations in algebra and physics. Elements of algebraic geometry.Text:
Artin, M. (2010). Algebra (2nd ed.). Upper Saddle River, NJ: PrenticeHall/ Pearson Education.Recommended Texts:
 Lang, S. (2005). Graduate Texts in Mathematics [Series, Bk. 211]. Algebra (3rded.). New York, NY: SpringerVerlag.
 Serre, J.P. (1977). Graduate Texts in Mathematics [Series, Bk. 42]. Linear Representations of Finite Groups. New York, NY: SpringerVerlag.
 Reid, M. (1989). London Mathematical Society Student Texts [Series]. Undergraduate Algebraic Geometry. New York, NY: Cambridge University Press.
 James, G., & Lieback, M. (1993). Cambridge Mathematical Textbooks [Series]. Representa
tions and Characters of Groups . New York, NY: Cambridge University Press.  Fulton, W., Harris, J. (2008). Graduate Texts in Mathematics/Readings in Mathematics [Series, Bk. 129]. Representation Theory: A First Course (Corrected ed.). New York, NY: SpringerVerlag.
 Sagan, B.E. (1991). Wadsworth & Brooks/Cole Mathematics Series [Series]. The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. Pacific Grove, CA: Wadsworth & Brooks/Cole.
 Brocker, T., & Dieck, T. (2003). Graduate Texts in Mathematics [Series, Bk. 98]. Representations of Compact Lie Groups. New York, NY: SpringerVerlag.


MATHGA.2210001 Introduction To Number Theory I
3 Points, Mondays, 11:0012:50PM, Yuri Tschinkel
Prerequisites:
Undergraduate elementary number theory, abstract algebra, including groups, rings and ideals, fields, and Galois theory (e.g. undergraduate Algebra I and II). A background in complex analysis, as well as in algebra, is required.
Description:
This graduate course will cover several analytic techniques in number theory, as well as properties of number fields and their rings of integers. Topics include: primes in arithmetic progressions, zetafunction, prime number theorem, number fields, rings of integers, Dedekind zetafunction, introduction to analytic techniques: circle method, sieves. 
MATHGA.2320001 Topology II
3 Points, Mondays, Wednesdays, 6:207:35PM, Sylvain Cappell
Description:
Homology and cohomology from simplicial, singular, cellular, axiomatic and differential form viewpoints. Axiomatic characterizations and applications to geometrical problems, including fixed points. Manifolds and Poincaré duality. Introduction to products and ring structures,vector bundles and, in particular, tangent bundles. 
MATHGA.2360001 Differential Geometry II
3 Points, Tuesdays, Thursdays, 11:0012:15PM, Robert Ji Wai Young
Description:
Differential Geometry II will focus on Riemannian geometry. Topics to be covered may include: second variation of arc length, Rauch comparison theorem and applications, Toponogov's theorem, invariant metrics on Lie groups, Morse theory, cut locus, the sphere theorem, complete manifolds of nonnegative curvature.
Recommended Texts:
 John Milnor, Morse Theory (Princeton University Press, 1963).
 John M. Lee, Riemannian Manifolds: An Introduction to Curvature (Springer, 1997)

MATHGA.2420001 Advanced Topics: Seminar In AOS
1.5 Points, Fridays, 3:455:00PM, Shafer Smith
Description TBA 
MATHGA.2420002 Advanced Topics: Topics In Conformal Geometry (1st Half Of Semester)
1.5 Points, Tuesdays, 1:253:15PM, Fengbo Hang
Description: We will discuss analytical problems related to fourth order equations in conformal geometry. In particular, we will study Q curvature equations and sharp inequalities.

MATHGA.2420003 Advanced Topics: Topics In Algebraic Geometry (2nd Half Of Semester)
1.5 Points, Tuesdays, 1:253:15PM, Alena Pirutka
Description: This is an introductory course in Algebraic Geometry

MATHGA.2420004 Advanced Topics In Applied Mathematics: Working Group In Modeling And Simulation
3 Points, Thursdays, 12:302:00PM, Jonathan Weare and Georg Stadler
Description TBA 
MATHGA.2420005 Advanced Topics In Analysis (1st Half Of Semeter)
1.5 Points, Tuesdays, 3:205:05PM, Percy Deift
Description: The goal of the course is to present M. Viazovska's recent proof of optical packing in eight dimensions. The prerequisite for the course is complex analysis, particularly the theory of elliptic functions. The course will follow the presentation of the proof of Viazovska's result in the recent book by D.Romik, Topics in Complex Analysis.

MATHGA.2420006 Advanced Topic: The Mumford Shah Functional In The Plane (2nd Half Of Semester)
3 Points, Thursdays, 3:205:05PM, Guido DePhilippis
The Mumford Shah functional has been introduced in the 80`s as tool for image denoising. Its rigorous study has lead to beautiful mathematical theories and several interesting problems are still unsolved. In this class I will review the classical theory and present some recent results

MATHGA.2420008 Advanced Topics In Analysis: Wavelets, Function Spaces, And Approximation Theory (2nd Half Of Semester)
1.5 Points, Tuesdays, 11:0012:50PM, Sinan Gunturk
Prerequisites: real analysis and introductory functional analysis, working knowledge of Fourier analysis.
Description: This course will present the theory of wavelets from the viewpoint of approximation theory. After covering the fundamentals of wavelet analysis and various wavelet constructions, we will study how smoothness spaces can be characterized by means of the wavelet series of their elements. We will then study the approximationtheoretical implications of these characterizations, specifically, how wavelets offer superior approximation guarantees via nonlinear approximation methods.

MATHGA.2420010 Advanced Topics In Applied Math: A Crash Course In Magnetohydrodynamics (1st Half Of Semester)
1.5 Points, Thursdays, 3:205:05PM, Alan Kaptanoglu
Description TBA 
MATHGA.2440001 Real Variables II
3 Points, Tuesdays, Thursdays, 9:3010:45AM, Jalal Shatah
Description TBA 
MATHGA.2470001 Ordinary Differential Equations
3 Points, Wednesdays, 11:0012:50PM, Esteban Tabak
Description TBA 
MATHGA.2500001 Partial Differential Equations
3 Points, Tuesdays, Thursdays, 2:003:15PM, Vlad Vicol
Prerequisites:
MATHGA 2490 (Introduction to Partial Differential Equations) and MATHGA 2430 (Real Variables). Masters students should consult the course instructor before registering for this class.
Description:
Undergraduate and MSlevel classes in PDE usually emphasize examples, involving solutions that are more or less explicit. This course does the opposite: it emphasizes more general methods, applicable to broad classes of PDE's. Topics to be covered include: tools from analysis (Fourier transform, distributions, and Sobolev spaces, including embedding and trace theorems); linear elliptic pde (weak solutions, regularity, Fredholm alternative, symmetry and selfadjointness, completeness of eigenfunctions; maximum principles and Perron's method; boundary integral methods); selected methods for solving nonlinear elliptic pde (fixed point theorems, variational methods); parabolic and hyperbolic pde (energy methods, semigroup methods, steepestdescent pde's); viscosity solutions of firstorder equations.
Main Texts:
L.C. Evans, Partial Differential Equations, American Mathematical Society
M. Renardy and R. Rogers, An Introduction to Partial Differential Equations, SpringerVerlag

MATHGA.2704001 Applied Stochastic Analysis
3 Points, Mondays, 11:0012:50PM, Jonathan Weare
Description TBA 
MATHGA.2708001 Algorithmic Trading & Quantitative Strategies
3 Points, Tuesdays, 7:109:00PM, Giuseppe Paleologo and Lee Maclin
Prerequisites:
Computing in Finance, and Risk and Portfolio Management, or equivalent.Description:
In this course we develop a quantitative investment and trading framework. In the first part of the course, we study the mechanics of trading in the financial markets, some typical trading strategies, and how to work with and model high frequency data. Then we turn to transaction costs and market impact models, portfolio construction and robust optimization, and optimal betting and execution strategies. In the last part of the course, we focus on simulation techniques, backtesting strategies, and performance measurement. We use advanced econometric tools and model risk mitigation techniques throughout the course. Handouts and/or references will be provided on each topic. 
MATHGA.2710001 Mechanics
3 Points, TDB TDB and TDB TDB and TDB TDB
Description TBA 
MATHGA.2751001 Risk & Portfolio Management
3 Points, Wednesdays, 7:109:00PM, Gordon Ritter
Description TBA 
MATHGA.2752001 Active Portfolio Management
3 Points, Wednesdays, 7:109:00PM, Jerome Benveniste
Prerequisites:
Risk & Portfolio Management and Computing in Finance.Description:
The first part of the course will cover the theoretical aspects of portfolio construction and optimization. The focus will be on advanced techniques in portfolio construction, addressing the extensions to traditional meanvariance optimization including robust optimization, dynamical programming and Bayesian choice. The second part of the course will focus on the econometric issues associated with portfolio optimization. Issues such as estimation of returns, covariance structure, predictability, and the necessary econometric techniques to succeed in portfolio management will be covered. Readings will be drawn from the literature and extensive class notes. 
MATHGA.2753001 Advanced Risk Management
3 Points, Wednesdays, 5:107:00PM, Ken Abbott and Irena Khrebtova
Prerequisites:
Financial Securities and Markets, and Computing in Finance or equivalent programming experience.Description:
The importance of financial risk management has been increasingly recognized over the last several years. This course gives a broad overview of the field, from the perspective of both a risk management department and of a trading desk manager, with an emphasis on the role of financial mathematics and modeling in quantifying risk. The course will discuss how key players such as regulators, risk managers, and senior managers interact with trading. Specific techniques for measuring and managing the risk of trading and investment positions will be discussed for positions in equities, credit, interest rates, foreign exchange, commodities, vanilla options, and exotic options. Students will be trained in developing risk sensitivity reports and using them to explain income, design static and dynamic hedges, and measure valueatrisk and stress tests. Students will create Monte Carlo simulations to determine hedge effectiveness. Extensive use will be made of examples drawn from real trading experience, with a particular emphasis on lessons to be learned from trading disasters.Text:
Allen, S.L. (2003). Wiley Finance [Series, Bk. 119]. Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk. Hoboken, NJ: John Wiley & Sons. 
MATHGA.2755001 Project & Presentation
3 Points, Wednesdays, 5:107:00PM, Petter Kolm
Description:
Students in the Mathematics in Finance program conduct research projects individually or in small groups under the supervision of finance professionals. The course culminates in oral and written presentations of the research results. 
MATHGA.2791001 Financial Securities And Markets
3 Points, Thursdays, 7:109:00PM, Mehdi Sonthonnax
Description TBA 
MATHGA.2793001 Dynamic Asset Pricing (2nd Half Of Semester)
3 Points, Tuesdays, 5:107:00PM, Bruno Dupire and Montacer Essid
Prerequisites:
Calculusbased probability, Stochastic Calculus, and a one semester course on derivative pricing (such as what is covered in Financial Securities and Markets).Description:
This is an advanced course on asset pricing and trading of derivative securities. Using tools and techniques from stochastic calculus, we cover (1) BlackScholesMerton option pricing; (2) the martingale approach to arbitrage pricing; (3) incomplete markets; and (4) the general option pricing formula using the change of numeraire technique. As an important example of incomplete markets, we discuss bond markets, interest rates and basic termstructure models such as Vasicek and HullWhite. It is important that students taking this course have good working knowledge of calculusbased probability and stochastic calculus. Students should also have taken the course “Financial Securities and Markets” previously. In addition, we recommend an intermediate course on mathematical statistics or engineering statistics as an optional prerequisite for this class. 
MATHGA.2798001 Interest Rate & Fx Models
3 Points, Thursdays, 5:107:00PM, Fabio Mercurio and Alexey Kuptsov
Prerequisites:
Financial Securities and Markets, Stochastic Calculus, and Computing in Finance (or equivalent familiarity with financial models, stochastic methods, and computing skills).Description:
The course is divided into two parts. The first addresses the fixedincome models most frequently used in the finance industry, and their applications to the pricing and hedging of interestbased derivatives. The second part covers the foreign exchange derivatives markets, with a focus on vanilla options and firstgeneration (flow) exotics. Throughout both parts, the emphasis is on practical aspects of modeling, and the significance of the models for the valuation and risk management of widelyused derivative instruments. 
MATHGA.2799001 Modeling And Risk Management Of Bonds And Securitized Products (2nd Half Of Semester)
1.5 Points, Mondays, 5:107:00PM, Rodney SunadaWong
Prerequisites:
Stochastic Calculus, and Financial Securities and Markets or equivalent knowledge of basic bond mathematics and bond risk measures (duration and convexity).Description:
This halfsemester course is designed for students interested in Fixed Income roles in frontoffice trading, market risk management, model development (“Quants”, “Strats”), or model validation.We begin by modeling the cash flows of a generic bond, emphasizing how the bond reacts to changes in markets, how traders may position themselves given their views on the markets, and how risk managers think about the risks of a bond. We then focus on Mortgages, covering the fundamentals of Residential Mortgages, and MortgageBacked Securities. Students will build pricing models for mortgages, passthroughs, sequentials and CMO’s that generate cash flows and that take into account interest rates, prepayments and credit spreads (OAS). The goals are for students to develop: (1) an understanding of how to build these models and how assumptions create “model risk”, and (2) a trader’s and risk manager’s intuition for how these instruments behave as markets change, and (3) a knowledge how to hedge these products. We will graph cash flows and changes in market values to enhance our intuition (e.g. in Excel, Python or by using another graphing tool).
In the course we also review the structures of CLO’s, Commercial Mortgage Backed Securities (CMBS), Auto Asset Backed Securities (ABS), Credit Card ABS, subprime mortgages and CDO’s and credit derivatives such as CDX, CMBX and ABX. We discuss the modeling risks of these products and the drivers of the Financial Crisis of 2008. As time permits, we touch briefly on Peertopeer / MarketPlace Lending.

MATHGA.2800001 Trading Energy Derivatives (1st Half Of Semester)
1.5 Points, Tuesdays, 5:107:00PM, Ilia Bouchouev
Prerequisites:
Financial Securities and Markets, and Stochastic Calculus.Description:
The course provides a comprehensive overview of most commonly traded quantitative strategies in energy markets. The class bridges quantitative finance and energy economics covering theories of storage, net hedging pressure, optimal risk transfer, and derivatives pricing models. Throughout the course, the emphasis is placed on understanding the behavior of various market participants and trading strategies designed to monetize inefficiencies resulting from their activities and hedging needs. We discuss in detail recent structural changes related to financialization of energy commodities, crossmarket spillovers, and linkages to other financial asset classes. Trading strategies include traditional risk premia, volatility, correlation, and higherorder options Greeks. Examples and case studies are based on actual market episodes using real market data. 
MATHGA.2801001 Advanced Topics In Equity Derivatives (2nd Half Of Semester)
1.5 Points, Wednesdays, 7:109:00PM, Alireza Javeheri
Prerequisites:
Financial Securities and Markets, Stochastic Calculus, and Computing in Finance or equivalent programming experience.Description:
This halfsemester course will give a practitioner’s perspective on a variety of advanced topics with a particular focus on equity derivatives instruments, including volatility and correlation modeling and trading, and exotic options and structured products. Some metamathematical topics such as the practical and regulatory aspects of setting up a hedge fund will also be covered. 
MATHGA.2802001 Market Microstructure (1st Half Of Semester)
1.5 Points, Mondays, 5:107:00PM, Merrell Hora
Prerequisites:
Financial Securities and Markets, Risk and Portfolio Management, and Computing in Finance or equivalent programming experience.Description:
This is a halfsemester course covering topics of interest to both buyside traders and sellside execution quants. The course will provide a detailed look at how the trading process actually occurs and how to optimally interact with a continuous limitorder book market.We begin with a review of early models, which assume competitive suppliers of liquidity whose revenues, corresponding to the spread, reflect the costs they incur. We discuss the structure of modern electronic limit order book markets and exchanges, including queue priority mechanisms, order types and hidden liquidity. We examine technological solutions that facilitate trading such as matching engines, ECNs, dark pools, multiple venue problems and smart order routers.
The second part of the course is dedicated pretrade market impact estimation, posttrade slippage analysis, optimal execution strategies and dynamic noarbitrage models. We cover AlmgrenChriss model for optimal execution, Gatheral’s nodynamicarbitrage principle and the fundamental relationship between the average response of the market price to traded quantity, and properties of the decay of market impact.
Homework assignments will supplement the topics discussed in lecture. Some coding in Java will be required and students will learn to write their own simple limitorderbook simulator and analyze real NYSE TAQ data.

MATHGA.2840003 Advanced Topics In Applied Math: Geometric Methods In Algorithm Design
3 Points, Tuesdays, 10:1512:15PM, Subhash Khot
Description TBA 
MATHGA.2901001 Essentials Of Probability
3 Points, Mondays, Wednesdays, 4:556:10PM, Yuri Bakhtin
Description TBA 
MATHGA.2902002 Stochastic Calculus Optional Problem Session
3 Points, Thursdays, 5:307:00PM, TBA
Description TBA 
MATHGA.2903001 Stochastic Calculus (2nd Half Of Semester)
3 Points, Mondays, 5:107:00PM, David Li
Description TBA 
MATHGA.2912001 Probability Theory II
3 Points, Mondays, Wednesdays, 2:003:15PM, Nina Holden
Prerequisites: Probability Limits Theorems 1
Description: Stochastic processes in continuous time. Brownian motion. Poisson process. Martingales and semimartingales. Stochastic integral. Stochastic differential equations. Markov processes. Connections with PDEs. Convergence of stochastic processes.
Main texts:
 Stochastic Processes by Bass
 J.F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus. Springer, 2016
 Stochastic Processes by Varadhan, Courant Lecture Series in Mathematics, volume 16
Other recommended texts:
 Theory of Probability and Random Processes by Koralov and Sinai
 Brownian Motion and Stochastic Calculus by Karatzas and Shreve
 D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, 1999

MATHGA.2962001 Mathematical Statistics
3 Points, Wednesdays, 5:007:30PM, Yisong Yang
Description TBA 
MATHGA.3004001 Atmospheric Dynamics
3 Points, Tuesdays, Thursdays, 3:304:45PM, Edwin Gerber
Description:
What effects the large scale circulation of the atmosphere? Like the antiquated heating system of a New York apartment, solar radiation unevenly warms the Earth, leading to gradients in energy in both altitude and latitude. But unlike the simple convection of air in your drafty home, the effects of rotation, stratification, and moisture lead to exotic variations in weather and climate, giving us something to chat about over morning coffee... and occasionally bringing modern life to a standstill.
The goals of this course are to describe and understand the processes that govern atmospheric fluid flow, from the Hadley cells of the tropical troposphere to the polar night jet of the extratropical stratosphere, and to prepare you for research in the climate sciences. Building on your foundation in Geophysical Fluid Dynamics, we will explore how stratification and rotation regulate the atmosphere's response to gradients in heat and moisture. Much of our work will be to explain the zonal mean circulation of the atmosphere, but in order to accomplish this we’ll need to learn a great deal about deviations from the zonal mean: eddies and waves. It turns out that eddies and waves, planetary, synoptic (weather system size) and smaller in scale, are the primary drivers of the zonal mean circulation throughout much, if not all, of the atmosphere.
There will also be a significant numerical modeling component to the course. You will learn how to run an atmospheric model on NYU's High Performance Computing facility, and then design and conduct experiments to test the theory developed in class for a final course project.
Recommended Texts:
Vallis, G.K. (2006). Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Largescale Circulation. New York, NY: Cambridge University Press.
Lorenz, E.N. (1967). The Nature and Theory of the General Circulation of the Atmosphere. World Meteorological Org.
Walker, G. (2007). An Ocean of Air: Why the Wind Blows and Other Mysteries of the Atmosphere. Orlando, FL: Houghton Mifflin Harcourt. 
MATHGA.3011001 Advanced Topics In AOS: DataDriven Geophysical Fluid Dynamics
3 Points, Mondays, 3:205:05PM, Laure Zanna and Sara Shamekh
Description: We will cover datadriven analysis techniques for geophysical fluid dynamics from a theoretical and applied perspective for atmosphere and oceanic phenomena.

MATHGA.3011002 Advanced Topics In AOS: Climate Change
3 Points, Mondays, 11:0012:50PM, Yi Zhang and Olivier Pauluis
Description: The first predictions of human induced global warming were made over a century ago, but the topic remains controversial despite the fact that the world has warmed 1 degree Celsius over the intervening years. In this course, we will investigate observational evidence as well as the physical and mathematical foundations upon which forecasts of future climate are based. What are the key uncertainties in the predictions, and what steps are required to reduce them? We will find that it is not the science of global warming that is controversial, but rather, what to do about it.
By reading through a mixture of historic and current studies, investigating key processes that affect the sensitivity of our planet to greenhouse gases, and exploring a hierarchy of climate models, this course will get you up to speed on the science of climate change. Grades will be based on a course project using a climate model to predict the impact of anthropogenic forcing on the Earth's climate. Particularly attention will be paid to establishing reproducible science and quantifying the uncertainty in your prediction.